Question: Solve for $x$ and $y$ using elimination. ${2x-y = 8}$ ${-5x+y = -29}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-3x = -21$ $\dfrac{-3x}{{-3}} = \dfrac{-21}{{-3}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {2x-y = 8}\thinspace$ to find $y$ ${2}{(7)}{ - y = 8}$ $14-y = 8$ $14{-14} - y = 8{-14}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {-5x+y = -29}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + y = -29}$ ${y = 6}$